An artificial magnetic honeycomb lattice that manifests a two-dimensional prototype of three-dimensional geometrically frustrated magnets yields a magnetism that has been intensively explored in recent times. The ice analogue of magnetism, spin ice, spin liquid, and exotic quantum mechanical properties of the resonant valence bond state have been of particular interest. The concept of an artificial honeycomb lattice or a two dimensional artificial structure was originally conceived to study the physics of spin ice state. From there, the exploration expanded to include a spectrum of the novel magnetism in geometrically frustrated magnets and a broad and tunable range of magnetic phenomena that would be difficult or impossible to achieve in natural materials. All of which became possible due to a recent proposal that suggests a magnetic moment or spin can be considered as a pair of magnetic charges of opposite polarities, as if it is a “dumbbell,” that interact via the Coulomb interaction. The direction of magnetic moment or spin points from the negative to the positive charge.
Extending the concept of magnetic charges to the artificial honeycomb lattice results in each vertex of the honeycomb possessing a net magnetic charge of ±3 or ±1 unit (see FIGS. 1 (a)-(c)). The charges ±3 and ±1 are associated to the peculiar spin configurations where the magnetic moment, aligned along the bond length due to the magnetostatic interaction, either points to or away from the vertex at the same time or, two of them point to (or away) from the vertex and one points away (or to) the vertex, respectively. These moment arrangements are also called “all-in” or “all-out” and “two-in & one-out” or vice-versa spin configurations. At sufficiently a high temperature, the lattice can be described as a paramagnetic gas consisting a random distribution of ±3 and ±1 magnetic charges. Recent theoretical calculations have shown that an artificial magnetic honeycomb lattice can undergo a variety of novel ordered regimes of correlated spins and magnetic charges of both fundamental and practical importance as a function of temperature, including long-range spin ice, entropy-driven magnetic charge-ordered state, and spin-order due to the spin chirality as a function of reducing temperature. At a low enough temperature, magnetic correlation is expected to develop into a spin solid state density in which the magnetization profile assumes a chiral vortex configuration involving six vertexes of the honeycomb lattice (see FIG. 1(d)). The spin solid state, manifested by the distribution of the pairs of vortex states of opposite chiralities across the lattice, provides a unique opportunity to realize a magnetic material with net zero entropy and magnetization for an ordered ensemble of magnetic moments.
The experimental efforts to realize the temperature dependent magnetic correlations in an artificial honeycomb lattice is limited due to the constraints of known nanofabrication methods based on electron-beam lithography (EBL). The EBL technique results in a small sample size with large connecting element (or bond of the honeycomb lattice), on the order of 500 nanometers to a few micrometers. Such large element sizes lead to the inter-elemental energy of 104-105 K. Therefore, thermal fluctuations cannot induce spin flip or induce the development of a new phase. Also, the small sample size rules out the application of macroscopic probes necessary for magnetic and electrical measurements that are key to exploring the magnetic phases in artificial honeycomb lattice.
A need still exists for a magnetic system that exhibits unidirectional current biasing at a modest current (resulting in reasonably small output power) without the application of magnetic field. Additionally, is desirable for any such device to operate at room temperature in order to facilitate its use in practical applications.